Variational Flow Models: Flowing in Your Style
CoRR(2024)
摘要
We introduce a variational inference interpretation for models of "posterior
flows" - generalizations of "probability flows" to a broader class of
stochastic processes not necessarily diffusion processes. We coin the resulting
models as "Variational Flow Models". Additionally, we propose a systematic
training-free method to transform the posterior flow of a "linear" stochastic
process characterized by the equation Xt = at * X0 + st * X1 into a straight
constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation
facilitates fast sampling along the original posterior flow without training a
new model of the SC flow. The flexibility of our approach allows us to extend
our transformation to inter-convert two posterior flows from distinct "linear"
stochastic processes. Moreover, we can easily integrate high-order numerical
solvers into the transformed SC flow, further enhancing sampling accuracy and
efficiency. Rigorous theoretical analysis and extensive experimental results
substantiate the advantages of our framework.
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